Jurusan Teknik Spil Fakultas Teknik Sipil dan Perencanaan

1. Jurusan Teknik Spil Fakultas Teknik Sipil dan Perencanaan Universitas Mercu Buana 12 MODUL 12 STRUKTUR BAJA II (2 SKS) 12.1 TUJUAN INSTRUKSIONAL 12.1.2 Tujuan Instruksional Umum (TIU) Memahami penerapan metoda LRFD dalam perencanaan balok komposit profil baja – pelat beton bertulang 12.1.2 Tujuan Instruksional Khusus (TIK) Dapat merumuskan dan menghitung kapasitas (resistance), faktor beban, faktor kapasitas, kriteria desain LRFD 12.2 MATERI KULIAH Pendekatan LRFD pada perencanaan Balok Komposit 12.3 POKOK BAHASAN Rumusan LRFD untuk Desain Balok Komposit, Asumsi Desain dan Definisi, Elastic dan Plastic Analysis, Desain Elemen Tekan, Desain Elemen Lentur 12.3.1 DESIGN ASSUMPTIONS AND DEFINITIONS Force Determination. Loads applied to an un-shored beam before the concrete has hardened are resisted by the steel section alone, and only loads applied after the concrete has hardened are considered as resisted by the composite section. It is usually assumed for design purposes that concrete has hardened when it attains 75 per cent of its design strength. In beams properly shored during construction, all loads may be assumed as resisted by the composite cross section. Loads applied to a continuous composite beam with shear connectors throughout its length, after the slab is cracked in the negative moment region, are resisted in that region by the steel section and by properly anchored longitudinal slab reinforcement. For purposes of plastic analysis all loads are considered resisted by the composite cross section, since a fully plastic strength is reached only after considerable yielding at the locations of plastic hinges. Elastic Analysis. The use of constant stiffness in elastic analyses of continuous beams is analogous to the practice in reinforced concrete design. The stiffness calculated using a weighted average of moments of inertia in the positive moment region and negative moment regions may take the following form: It =a Ipos+ b Ineg Where http://www.mercubuana.ac.id

2. 12.3.2 COMPRESSION MEMBERS Limitations (1) The lower limit of four percent on the cross-sectional area of structural steel differentiates between composite and reinforced concrete columns. If the area is less than four percent, a column with a structural steel core should be designed as a reinforced concrete column. (2) The specified minimum quantity of transverse and longitudinal reinforcement in the encasement should be adequate to prevent severe spalling of the surface concrete during fires. (3) Very little of the supporting test data involved concrete strengths in excess of 6 ksi (41 MPa), even though the cylinder strength for one group of four columns was 9.6 ksi (66 MPa). Normal weight concrete is believed to have been used in all tests. Thus, the upper limit of concrete strength is specified as 8 ksi (55MPa) for normal weight concrete. A lower limit of 3 ksi (21 MPa) is specified for normal weight concrete and 4 ksi (28 MPa) for lightweight concrete to encourage the use of good quality, yet readily available, grades of structural concrete. (4) In addition to the work of Bridge and Roderick (1978), SSRC Task Group 20 (1979), and Galambos and Chapuis (1980), recent work by Kenny, Bruce, and Bjorhovde (1994) has shown that due to concrete confinement effects, the previous limitation of 55 ksi (380 MPa) for the maximum steel yield stress is highly restrictive. Further, the most commonly used reinforcing steel grade has a yield stress of 60 ksi (415 MPa). The increase is therefore a rational recognition of material properties and structural behavior. The 60 ksi (415 MPa) limitation for the yield stress is very conservative for tubular composite columns, where the concrete confinement provided by the tube walls is very significant. Kenny et al. have proposed raising the value of Fy for such columns to whatever the yield stress is for the steel grade used, but not higher than 80 ksi (550 MPa). (5) The specified minimum wall thicknesses are identical to those in the 1995 ACI Building Code (1995). The purpose of this provision is to prevent buckling of the steel pipe or HSS before yielding. Design Strength The procedure adopted for the design of axially loaded composite columns is described in detail in Galambos and Chapuis (1980). It is based on the equation for the strength of a short column derived in Galambos and Chapuis (1980), and the same reductions for slenderness as those specified for steel columns in Section E2. The design follows the same path as the design of steel columns, except that the yield stress of structural steel, the modulus of elasticity of steel, and the radius of gyration of the steel section are modified to account for the effect of concrete and longitudinal reinforcing bars. A detailed explanation of the origin of these modifi cations may be found in SSRC Task Group 20 (1979). Galambos and Chapuis (1980) includes comparisons of the design procedure with 48 tests of axially loaded stub columns, 96 tests of concrete-filled pipes or tubing (HSS), and 26 tests of concrete-encased steel shapes. The mean ratio of the test failure loads to the predicted strengths was 1.18 for all 170 tests, and the corresponding coefficient of variation was 0.19. Columns with Multiple Steel Shapes http://www.mercubuana.ac.id

3. Positive Flexural Design Strength. Flexural strength of a composite beam in the positive moment region may be limited by the plastic strength of the steel section, the concrete slab, or shear connectors. In addition, web buckling may limit flexural strength if the web is slender and a significantly large portion of the web is in compression. According to Table B5.1, local web buckling does not reduce the plastic strength of a bare steel beam if the beam depth-to-web thickness ratio is not larger than 3.76 / F In the absence of web buckling research on composite beams, the same ratio is conservatively applied to composite beams. Furthermore, for more slender webs, the LRFD Specification conservatively adopts first yield as the flexural strength limit. In this case, stresses on the steel section from permanent loads applied to unshored beams before the concrete has hardened must be superimposed on stresses on the composite section from loads applied to the beams after hardening of concrete. In this superposition, all permanent loads should be multiplied by the dead load factor and all live loads should be multiplied by the live load factor. For shored beams, all loads may be assumed as resisted by the composite section. When first yield is the flexural strength limit, the elastic transformed section is used to calculate stresses on the composite section. The modular ratio n = E /EC used to determine the transformed section depends on the specified unit weight and strength of concrete. Note that this procedure for compact beams differs from the requirements of Section 12 of the 1989 AISC ASD Specification. Plastic Stress Distribution for Positive Moment. When flexural strength is determined from the plastic stress distribution shown in Figure C-13.1, the compression force C in the concrete slab is the smallest of: For a non-hybrid steel section, Equation C-13- 1 becomes C=AsFy where http://www.mercubuana.ac.id